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#400 by meberbs on 23 Jun, 2017 22:16
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Radiation pressure as you described is for the photons that are reflected not absorbed. The energy losses are almost entirely from absorbed photons (which apply half the radiation pressure.). The absorbed photons are not re-emitted. Reflected photons do not change frequency (and therefore energy) unless there is a difference in velocity between the source and what it is reflected from. There is a tiny effect from the radiation pressure if it is causing acceleration as well. If you go look up some of my earliest posts on this site you would see I calculated it and the effect is negligible.The cavity photons, once emitted by the coupler / antenna, immediately start to lose energy to wall eddy current heating. As they do that their wavelength permanently ref shifts as their frequency drops.
In case there are any bystanders curious, the flaw in the above is that it ignores that the decrease in energy over time would be from individual photons being absorbed. If the above were true it would obviously show up in various experiments such as a 2 port measurement tracking the energy stored in the cavity. Also, trivially, if you went into a dark room and shined a blue light on a black (but not 100% absorptive) piece of paper the above logic implies that the reflected light would be red.
Here is an interesting table based on an individual 2.45GHz photon losing 63.2% of it's energy every TC and red shifting inside the cavity as attached.
Of course their lost eddy current heating energy is remitted as much higher freq and energy IR photons.
When cavity photons are absorbed by the electrons on surface metallic atoms, they are also reemitted back into the cavity The process is called radiation pressure. Any lost energy and/or momentum transfer results in the reemittted photon being red shifted to reflects it's lower level of energy.
A photon can not lose energy and have the same wavelength or frequency. As it loses energy, it red shifts. Photon wavelength = hc / photon energy.
Once a cavity is filled, the per cycle J input from the Rf source equals the per cycle photon J loss due to all loss sources. When the Rf input into the cavity is stopped, the stored photon energy decays over 5 x TC and the photon wavelengths increase.
The predominant photon energy loss in a cavity is from the photon's H fields inducing eddy current flow into the metallic walls and end plates which results in ohmic heating. The energy to generate the heating is sourced from the photon's energy. Photon absord and emit events are not required to generate skin depth eddy currents and related heating.
Don't believe shinning a blue light on a black piece of paper has anything to do with the above, especially as there is no eddy current heating involved. However if the event occurred in space and the black paper gained momentum and energy from the blue light, the reemitted light would be very slighlty red shifted to reflect the lost momentum and energy.
Radiation pressure = (2 * E) / c
The 2 represents 2 momentum and energy transfer, from photon to mass, events. 1st for the absord event and 2nd for the emit event. -
#401 by spupeng7 on 24 Jun, 2017 01:21
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Thanks meberbs,
We are in complete agreement here. I did not used any modifiers like Euclidean or orthogonal, or even linear. The dimensions in general are curved, non-orthogonal, and mixed in with the fourth (temporal) dimension. All of the dimensions exist, 3 spatial and 1 temporal, and you need all of them to properly describe the motions of objects (which is the essence of physics in a way). There is no sensible way to boil 4 dimensions down to just 1.
meberbs,
(...)
You can't just ignore the existence of spatial dimensions. They obviously exist,
(...)
please forgive this extraction from your argument but SR exposes a flaw in the notion of orthogonal spatial dimensions. You may define them but they cannot retain their orthogonality across a dilation of time.
Distance and direction remain relevant descriptors but Euclidian space is redundant no matter how well Rutherford defines it.
do we also agree that those four dimensions are descriptors of 'spacetime' which have no independent existence, that the three spatial dimensions are entirely artificial constructs which have limited application to physical science?
Can spacetime be reconciled with both dynamic and electromagnetic action without the incorporation of complex numbers as fundamental units of that physical science? -
#402 by spupeng7 on 24 Jun, 2017 01:27
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With fully automated navigation for collision avoidance and law abidance, I see no reason why 'flying cars' should not have complete freedom of movement.Imagine space access to be just as mundane as air flight is today.
A trip to the moon, to visit you son or daughter who's working there as an astro-geologist.
A 2week flight to mars to conclude a business deal
A Jupiter flyby honeymoon trip...
Why would I need a flying car when my grandchildren could be standing on Europa (the moon) ?
With a pressurized and confortable flying car, at home, you could walk down your backyard, open the door, sit down, and ask Siri to go directly to the Moon, Mars or Europa. No need to go to a spaceport, register and wait for a shuttle.
But even if such trips were technologically feasible at a personal level, probably every country regulation would prevent anybody to travel outside their airspace and even more the boundary of Earth atmosphere. Not as long as countries of Earth still undergo political, economical, religious and resource-based conflicts, with territory colonization, oil wars, terror attacks and massive migration problems. I can't imagine this era to happen for humans of Earth, sadly.
You are not going to be allowed to fly over houses or neighborhoods and FAA rules will apply. Flying cars will have to be flown from airports of some kind, not just anywhere to anywhere. Airspace and it's uses will be tightly controlled. -
#403 by spupeng7 on 24 Jun, 2017 01:39
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(...)
meberbs,
Radiation pressure as you described is for the photons that are reflected not absorbed. The energy losses are almost entirely from absorbed photons (which apply half the radiation pressure.). The absorbed photons are not re-emitted. Reflected photons do not change frequency (and therefore energy) unless there is a difference in velocity between the source and what it is reflected from. There is a tiny effect from the radiation pressure if it is causing acceleration as well. If you go look up some of my earliest posts on this site you would see I calculated it and the effect is negligible.
is it not true that absorption of radiation engenders a current in the reflector, even when that radiation is re-emitted. A more extensive reflecting surface might then contain both the energy of that radiation and the inertia imparted by its radiation pressure, for longer than a less extensive reflecting surface might do.
Is this not a potential explanation for emdrive thrust? -
#404 by eh90 on 24 Jun, 2017 07:55
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Would it be possible to use the magnetism found within the heliosphere to boost the thrust? Or the reactions between planetary magnetic fields and the HMF? I would imagine this would only result in a net gain of a few millinewtons, but extra thrust is extra thrust.
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#405 by Bob012345 on 24 Jun, 2017 19:31
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Would it be possible to use the magnetism found within the heliosphere to boost the thrust? Or the reactions between planetary magnetic fields and the HMF? I would imagine this would only result in a net gain of a few millinewtons, but extra thrust is extra thrust.
You certainly can design spacecraft to harness those fields directly but that's another topic altogether.
http://spacenews.com/experiment-designed-harness-magnetic-field-propulsion/
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#406 by flux_capacitor on 24 Jun, 2017 20:23
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Would it be possible to use the magnetism found within the heliosphere to boost the thrust? Or the reactions between planetary magnetic fields and the HMF? I would imagine this would only result in a net gain of a few millinewtons, but extra thrust is extra thrust.
You certainly can design spacecraft to harness those fields directly but that's another topic altogether.
http://spacenews.com/experiment-designed-harness-magnetic-field-propulsion/
Dear eh90, we don't currently understand how the EmDrive works, and we don't know if it works at all (the tiny thrusts measured with experiments so far could be systematic experimental errors). If it works, we don't know if the emDrive depends on such things as Earth's magnetic field, or Earth's gravitational potential in its surroundings, so we don't know if it could also work in deep space where there are no such fields. Hence this kind of question, although interesting, is really premature. -
#407 by ThereIWas3 on 24 Jun, 2017 21:42
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With fully automated navigation for collision avoidance and law abidance, I see no reason why 'flying cars' should not have complete freedom of movement.
All current aircraft are restricted to being 1,000 feet from any inhabited structure or large crowd of people, or 500 feet from open ground. And if an airplane or helicopter loses power, it descends relatively slowly and under full control. A flying car using a mechanism like EM (assuming you could get that much lift from it) becomes a brick if the power fails. And automatic parachutes (some small aircraft actually have these) need altitude to work and are not very controllable. Watch out for those high tension lines... And then if the wind is blowing... -
#408 by spupeng7 on 25 Jun, 2017 01:18
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Thanks ThereIWas3,With fully automated navigation for collision avoidance and law abidance, I see no reason why 'flying cars' should not have complete freedom of movement.
All current aircraft are restricted to being 1,000 feet from any inhabited structure or large crowd of people, or 500 feet from open ground. And if an airplane or helicopter loses power, it descends relatively slowly and under full control. A flying car using a mechanism like EM (assuming you could get that much lift from it) becomes a brick if the power fails. And automatic parachutes (some small aircraft actually have these) need altitude to work and are not very controllable. Watch out for those high tension lines... And then if the wind is blowing...
all this depends upon what specific thrust can be achieved. If propulsion is a small fraction of MTOW then triple redundancy could be employed. Who was it said "... predicting the future is like driving a car backwards in a heavy fog ..." -
#409 by ThinkerX on 25 Jun, 2017 03:38
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Ok.
Shell said her experimental efforts indicate some sort of purely magnetic explanation for how the EM Drive works - perhaps something similar to Dust in the Winds proposal.
However, much of the recent theory work seems oriented towards the Woodward/Mach effect or something close to it. (Rodal, among others.)
So, are these positions mutually exclusive? Or can they be combined somehow?
I seem to recollect a paper mentioned at the Estes Confab that linked internal magnetic effects of the frustum to Woodward/Mach, but I also have a hazy recollection there were issues with this paper. -
#410 by SeeShells on 25 Jun, 2017 13:45
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Ok.
Shell said her experimental efforts indicate some sort of purely magnetic explanation for how the EM Drive works - perhaps something similar to Dust in the Winds proposal.
However, much of the recent theory work seems oriented towards the Woodward/Mach effect or something close to it. (Rodal, among others.)
So, are these positions mutually exclusive? Or can they be combined somehow?
I seem to recollect a paper mentioned at the Estes Confab that linked internal magnetic effects of the frustum to Woodward/Mach, but I also have a hazy recollection there were issues with this paper.
This is an excellent write-up of the Advanced Propulsion Workshop and the source material for my reply. I was honored to attend.
Estes Park Advanced Propulsion Workshop
19 —22 September 2016
Estes Park, Colorado, USA
edited by
H. Fearn L. L. Williams
Relevant reading materials to consider first.
Intro to MEP
Introduction to “ Mach Effect Propulsion” in Appendix D – J.J.A. Rodal Page 127
Dr. Rodal's excellent paper on the MEGA Mach Effect starts at page 282
http://ssi.org/wp-content/uploads/2017/02/ssi_estes_park_proceedings_201609.pdf
(warning... a PDF but worth it to read)
Coupling the EMDrive to Mach Effects with a paper (his presentation via Skype)
Theory of the EM-drive Based on Mach-Lorentz Theory – J.-P. Montillet Page 111
---------------
There could be a link between the Mach Effects using the manipulation of the EM field environment of the EMDrive, although further testing is in order. It needs to be noted that anomalous thrusts have also been reported without specifically trying to enhance a Mach effect in a EMDrive, which is part of the quandary and raises the question, are we seeing more than one effect take place? Also the TM mode cited by J.-P. Montillet in his theory isn't the only mode (TE is the other) that apparent thrust happens. That needs to be addressed along with other issues.
If it can be built where the Mach Effects can be established in the asymmetrical EMDrive cavity by manipulation if the fields and the resultant actions it could mean that the use of PZT like materials which need to operate over 2.5x10^13 or 25 Trillion pulses
or greater during a lifetime wouldn't need to be used, or they could be used in a more efficient manner. This direction could lead to a more materials stable device with a potential for a longer life and higher thrusts.
My Very Best,
Shell
PS: Sorry I haven't re-written up the current work like I said, I had other pressing issues arise. I'll try to get it out in a post again.
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#411 by ThinkerX on 25 Jun, 2017 21:01
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Quote
There could be a link between the Mach Effects using the manipulation of the EM field environment of the EMDrive, although further testing is in order. It needs to be noted that anomalous thrusts have also been reported without specifically trying to enhance a Mach effect in a EMDrive, which is part of the quandary and raises the question, are we seeing more than one effect take place? Also the TM mode cited by J.-P. Montillet in his theory isn't the only mode (TE is the other) that apparent thrust happens. That needs to be addressed along with other issues.
If it can be built where the Mach Effects can be established in the asymmetrical EMDrive cavity by manipulation if the fields and the resultant actions it could mean that the use of PZT like materials which need to operate over 2.5x10^13 or 25 Trillion pulses or greater during a lifetime wouldn't need to be used, or they could be used in a more efficient manner. This direction could lead to a more materials stable device with a potential for a longer life and higher thrusts.
A few weeks back - an eternity in these threads - I posted a suggestion:
The Mach Effect relies on the gravitational influences of 'distant bodies' in order to function.
However, there is one nearby astronomical body whose gravitation causes major effects on earth: the moon. Lunar tides, in places, alter ocean levels at the coastlines by tens of feet. That seems like a pretty potent source.
Perhaps some of the larger anomalous 'thrusts' are linked to the lunar cycle, and the devices lunar orientation. Or to put it another way:
what would the local high (or low) tide have been at Shell's location during the times of her tests?
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#412 by meberbs on 25 Jun, 2017 21:15
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Thanks meberbs,
I am not entirely clear what you mean by the first part. We might be in agreement, but the way I would say it is that the ultimate choice of reference frame is arbitrary, so any single representation of spacetime with a chosen reference frame is artificial, but it is still describing something real, as there are rigorous equations that allow transformation of one description to any of the infinite number of other valid descriptions of that spacetime, and there is a further, (much larger) infinity of descriptions that don't describe that spacetime.
do we also agree that those four dimensions are descriptors of 'spacetime' which have no independent existence, that the three spatial dimensions are entirely artificial constructs which have limited application to physical science?
Can spacetime be reconciled with both dynamic and electromagnetic action without the incorporation of complex numbers as fundamental units of that physical science?
I am really not sure what you mean by the last question. The only time complex numbers are really fundamental to a physical theory is in quantum, and even then, the physically measurable parts are pure real. There is a representation of coordinates for special relativity where the metric has a -1 for the time axis, which effectively means an "imaginary" basis vector for time. I think this is a helpful way of thinking about spacetime, but I don't think it is necessary, as you can do all of the required math without needing complex numbers. -
#413 by Monomorphic on 25 Jun, 2017 21:21
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The last month and a half have been very busy for me. I've been traveling some, and have had other projects wrapping up and some new projects beginning that are very time consuming. But work still continues on my tests.
I had to revert to the custom copper/stainless terminal block as it is easier to isolate the main leads while probing for errant EM fields. This configuration also seems to have less noise than the previous. I hope to complete a series of 2.5W tests at intervals along the return loss trace to see if there is any difference in displacement. After that, onward to 30W.
I have also purchased the Prusa i3 MK2S 3D printer. It arrives in 7 weeks! There is a huge back order as it is in high demand right now. I will be using it to fabricate spherical end plates.
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#414 by SeeShells on 25 Jun, 2017 21:23
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Interesting thought although.QuoteThere could be a link between the Mach Effects using the manipulation of the EM field environment of the EMDrive, although further testing is in order. It needs to be noted that anomalous thrusts have also been reported without specifically trying to enhance a Mach effect in a EMDrive, which is part of the quandary and raises the question, are we seeing more than one effect take place? Also the TM mode cited by J.-P. Montillet in his theory isn't the only mode (TE is the other) that apparent thrust happens. That needs to be addressed along with other issues.
If it can be built where the Mach Effects can be established in the asymmetrical EMDrive cavity by manipulation if the fields and the resultant actions it could mean that the use of PZT like materials which need to operate over 2.5x10^13 or 25 Trillion pulses or greater during a lifetime wouldn't need to be used, or they could be used in a more efficient manner. This direction could lead to a more materials stable device with a potential for a longer life and higher thrusts.
A few weeks back - an eternity in these threads - I posted a suggestion:
The Mach Effect relies on the gravitational influences of 'distant bodies' in order to function.
However, there is one nearby astronomical body whose gravitation causes major effects on earth: the moon. Lunar tides, in places, alter ocean levels at the coastlines by tens of feet. That seems like a pretty potent source.
Perhaps some of the larger anomalous 'thrusts' are linked to the lunar cycle, and the devices lunar orientation. Or to put it another way:
what would the local high (or low) tide have been at Shell's location during the times of her tests?
https://en.wikipedia.org/wiki/RF_resonant_cavity_thruster#Mach_effectQuoteIn a fully Machian general relativity theory like the Hoyle–Narlikar theory of gravity, inertia is a physical gravitational interaction of matter with the rest of the mass-energy in the universe, through an action at a distance instantaneous radiative reaction field. In the theory, a mass changing effect suitable for propulsion emerges from the general equation of motion.[91]
In non-scientific terms it means the whole enchilada... i.e. everything in the universe.
https://en.wikipedia.org/wiki/Hoyle%E2%80%93Narlikar_theory_of_gravity
My Very Best,
Shell -
#415 by Rodal on 25 Jun, 2017 22:27
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Thanks meberbs,
I am not entirely clear what you mean by the first part. We might be in agreement, but the way I would say it is that the ultimate choice of reference frame is arbitrary, so any single representation of spacetime with a chosen reference frame is artificial, but it is still describing something real, as there are rigorous equations that allow transformation of one description to any of the infinite number of other valid descriptions of that spacetime, and there is a further, (much larger) infinity of descriptions that don't describe that spacetime.
do we also agree that those four dimensions are descriptors of 'spacetime' which have no independent existence, that the three spatial dimensions are entirely artificial constructs which have limited application to physical science?
Can spacetime be reconciled with both dynamic and electromagnetic action without the incorporation of complex numbers as fundamental units of that physical science?
I am really not sure what you mean by the last question. The only time complex numbers are really fundamental to a physical theory is in quantum, and even then, the physically measurable parts are pure real. There is a representation of coordinates for special relativity where the metric has a -1 for the time axis, which effectively means an "imaginary" basis vector for time. I think this is a helpful way of thinking about spacetime, but I don't think it is necessary, as you can do all of the required math without needing complex numbers.
I think (spupeng7 should explain himself what he means of course
) that by imaginary time spupeng7 may be referring to this https://en.wikipedia.org/wiki/Imaginary_time which is a concept that was basically popularized by Hawking in his 1988 book "A Brief History of Time" in an attempt at a Quantum Gravity theory. By this imaginary time Hawking is not at all referring to a representation of coordinates for special relativity where the metric has a -1 for the time axis, which effectively means an "imaginary" basis vector for time. I think this is a helpful way of thinking about spacetime, but I don't think it is necessary, as you can do all of the required math without needing complex numbers
which is a different concept.
This different (older concept) is the representation xo= i c t which is OK, and perhaps helpful when used in Special Relativity but not (when solving problems) in General Relativity.
Meberbs you are 100% correct that you can do all the necessary math for Einstein's Relativity without using complex numbers. Actually, for General Relativity you better use real numbers for the time coordinate:
This representation is (justifiably in my opinion) called abominable by Kip Thorne when it is used for General Relativity, who calls textbooks that try to do General Relativity using it as abominable, because while one can get away with xo= i c t in (perfectly flat) Minkowski spacetime (in other words, in Special Relativity), one cannot readily solve General Relativity problems using this imaginary time coordinate xo= i c t representation. Hence in General Relativity physicists (and all advanced textbooks) use just xo= t, and the price one pays for this is to have to agree on a consistent signature for the metric of spacetime , for example spacelike [-,+,+,+] (mostly pluses) (used by Wikipedia, and the textbooks of Wald, and also Misner, Thorne and Wheeler) or timelike [+,-,-,-] (mostly minuses) (used by Leonard Susskind, Witten, and by Landau and Lifshitz). The front inside cover of Misner Thorne and Wheeler lists conventions for metric signature, for the Riemann Tensor, for the Einstein Tensor, and for the use of Greek and Latin indices and lists 34 texts and what conventions they use. And then spells out on the facing side where the signs go.
So going back to Hawking's use of "imaginary time," it was a concept used for some versions of Quantum Gravity, Hawking, at the time (30 years ago ), believed that a quantum gravity theory could be successfully developed in this way. Imaginary time is obtained from real time via a Wick rotation in the complex plane (https://en.wikipedia.org/wiki/Wick_rotation ). He thought that it was possible to avoid singularities in this Wick rotated space. His views (popularized in a "Brief History of Time") are technically summarized in J. B. Hartle and S. W. Hawking, "Wave function of the Universe" Phys. Rev. D 28 (1983) 2960–2975. [
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.28.2960 ] Also see: https://en.wikipedia.org/wiki/Hartle%E2%80%93Hawking_state .
It is by now (2017) an old approach that does not work well in general because of many difficulties. I may be wrong but I wonder whether even Hawking is still pursuing this approach to Quantum Gravity.
If somebody disagrees, please specify a mathematical solution to General Relativity using imaginary time, that cannot be done even easier with real numbers for the time coordinate as used by Wald, Misner-Thorpe-Wheeler, Witten, or Landau-Lifshitz.
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#416 by demofsky on 25 Jun, 2017 23:29
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The last month and a half have been very busy for me. I've been traveling some, and have had other projects wrapping up and some new projects beginning that are very time consuming. But work still continues on my tests.
I have to wonder, if as a last test, before transitioning to 30W whether it would be worthwhile to try TE011 on your rig to see if there is improved thrust as Phil is claiming. If you could get TE011 going reasonably it would be a great A/B test on a well characterized test rig.
I had to revert to the custom copper/stainless terminal block as it is easier to isolate the main leads while probing for errant EM fields. This configuration also seems to have less noise than the previous. I hope to complete a series of 2.5W tests at intervals along the return loss trace to see if there is any difference in displacement. After that, onward to 30W.
I have also purchased the Prusa i3 MK2S 3D printer. It arrives in 7 weeks! There is a huge back order as it is in high demand right now. I will be using it to fabricate spherical end plates. -
#417 by Monomorphic on 26 Jun, 2017 00:08
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The last month and a half have been very busy for me. I've been traveling some, and have had other projects wrapping up and some new projects beginning that are very time consuming. But work still continues on my tests.
I have to wonder, if as a last test, before transitioning to 30W whether it would be worthwhile to try TE011 on your rig to see if there is improved thrust as Phil is claiming. If you could get TE011 going reasonably it would be a great A/B test on a well characterized test rig.
I had to revert to the custom copper/stainless terminal block as it is easier to isolate the main leads while probing for errant EM fields. This configuration also seems to have less noise than the previous. I hope to complete a series of 2.5W tests at intervals along the return loss trace to see if there is any difference in displacement. After that, onward to 30W.
I have also purchased the Prusa i3 MK2S 3D printer. It arrives in 7 weeks! There is a huge back order as it is in high demand right now. I will be using it to fabricate spherical end plates.
TE011 is quite a bit lower in frequency than TE013. While my signal generator is capable of generating those frequencies, the 2.4 Ghz amplifiers are not. I would need another main amplifier to test TE011 with the current cavity.
However, the new 3D printer will allow me to fabricate a cavity specifically designed for TE011 at 2.45Ghz with the highly curved end plates seen recently. -
#418 by spupeng7 on 26 Jun, 2017 03:00
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Thanks meberbs,
I am not entirely clear what you mean by the first part. We might be in agreement, but the way I would say it is that the ultimate choice of reference frame is arbitrary, so any single representation of spacetime with a chosen reference frame is artificial, but it is still describing something real, as there are rigorous equations that allow transformation of one description to any of the infinite number of other valid descriptions of that spacetime, and there is a further, (much larger) infinity of descriptions that don't describe that spacetime.
do we also agree that those four dimensions are descriptors of 'spacetime' which have no independent existence, that the three spatial dimensions are entirely artificial constructs which have limited application to physical science?
Can spacetime be reconciled with both dynamic and electromagnetic action without the incorporation of complex numbers as fundamental units of that physical science?
I am really not sure what you mean by the last question. The only time complex numbers are really fundamental to a physical theory is in quantum, and even then, the physically measurable parts are pure real. There is a representation of coordinates for special relativity where the metric has a -1 for the time axis, which effectively means an "imaginary" basis vector for time. I think this is a helpful way of thinking about spacetime, but I don't think it is necessary, as you can do all of the required math without needing complex numbers.
I think (spupeng7 should explain himself what he means of course ) that by imaginary time spupeng7 may be referring to this https://en.wikipedia.org/wiki/Imaginary_time which is a concept that was basically popularized by Hawking in his 1988 book "A Brief History of Time" in an attempt at a Quantum Gravity theory. By this imaginary time Hawking is not at all referring to a representation of coordinates for special relativity where the metric has a -1 for the time axis, which effectively means an "imaginary" basis vector for time. I think this is a helpful way of thinking about spacetime, but I don't think it is necessary, as you can do all of the required math without needing complex numbers
which is a different concept.
This different (older concept) is the representation xo= i c t which is OK, and perhaps helpful when used in Special Relativity but not (when solving problems) in General Relativity.
Meberbs you are 100% correct that you can do all the necessary math for Einstein's Relativity without using complex numbers. Actually, for General Relativity you better use real numbers for the time coordinate:
This representation is (justifiably in my opinion) called abominable by Kip Thorne when it is used for General Relativity, who calls textbooks that try to do General Relativity using it as abominable, because while one can get away with xo= i c t in (perfectly flat) Minkowski spacetime (in other words, in Special Relativity), one cannot readily solve General Relativity problems using this imaginary time coordinate xo= i c t representation. Hence in General Relativity physicists (and all advanced textbooks) use just xo= t, and the price one pays for this is to have to agree on a consistent signature for the metric of spacetime , for example spacelike [-,+,+,+] (mostly pluses) (used by Wikipedia, and the textbooks of Wald, and also Misner, Thorne and Wheeler) or timelike [+,-,-,-] (mostly minuses) (used by Leonard Susskind, Witten, and by Landau and Lifshitz). The front inside cover of Misner Thorne and Wheeler lists conventions for metric signature, for the Riemann Tensor, for the Einstein Tensor, and for the use of Greek and Latin indices and lists 34 texts and what conventions they use. And then spells out on the facing side where the signs go.
So going back to Hawking's use of "imaginary time," it was a concept used for some versions of Quantum Gravity, Hawking, at the time (30 years ago ), believed that a quantum gravity theory could be successfully developed in this way. Imaginary time is obtained from real time via a Wick rotation in the complex plane. He thought that it was possible to avoid singularities in this Wick rotated space. His views (popularized in a "Brief History of Time") are technically summarized in J. B. Hartle and S. W. Hawking, "Wave function of the Universe" Phys. Rev. D 28 (1983) 2960–2975. [
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.28.2960 ] Also see: https://en.wikipedia.org/wiki/Hartle%E2%80%93Hawking_state .
It is by now (2017) an old approach that does not work well in general because of many difficulties. I may be wrong but I wonder whether even Hawking is still pursuing this approach to Quantum Gravity.
If somebody disagrees, please specify a mathematical solution to General Relativity using imaginary time, that cannot be done even easier with real numbers for the time coordinate as used by Wald, Misner-Thorpe-Wheeler, Witten, or Landau-Lifshitz.
Thankyou meberbs, Shell and Dr Rodal,
while out of my depth with the math of General Relativity it is clear to me that a functioning emdrive indicates interaction with the wider universe, all of it that is old enough to be within the range, ict. What I propose is that all interaction is electromagnetic and that it occurs across separations that only exist from point perspectives. A covariant perspective, as I understand it, requires coincidence of locations in spacetime which are remote from one another from the point perspective.
The solution I visualize is; gravity and inertia consequent upon the sum of interaction with everything else by charge interactions mediated by time dilation; electromagnetic action being the consequence of the sum of individual interactions of pairs of charges also mediated by time dilation but limited to those in resonance with uninterrupted line of sight.
No mathematical system yet resolves complex time, charge, mass, distance and direction, as the useful descriptors of physical force and energetic interaction. All available mathematical systems employ spatial dimensions which loose their orthogonality and become oppressively complicated with proximity to time dilation. My suggestion is that a system incorporating complex time may be capable of explaining the physical forces without the paradox which is glaringly obvious to me whenever I try to understand QM or GR.
I am convinced that a seamless explanation for physical interaction is possible and that the emdrive can point us in the direction required to find it. Surely it will be Machian. How can it not incorporate either complex time or some other resolution for remote action between charges? Thank you all for your patience with my struggles to understand this.
Q: is the reference https://journals.aps.org/prd/abstract/10.1103/PhysRevD.28.2960 available without a paywall anywhere? -
#419 by Chrochne on 26 Jun, 2017 07:37
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Hi guys,
Just found out following information about the EmDrive development.
BBC made a report about the Gilo Industries on 4.4. 2017 that I missed (shame on me!). They spoke a bit about that new investment from the Kuang-Chi this year.
Mr. Gilo also mentions something interesting. That "they can not yet speak about the best thing they made" and that they may reveal it later this year.
Of course it can be anything. They work on many interesting project, but given the fact, that we know about their cooperation with Mr. Shawyer there is some probability it can be the EmDrive.
This supports, that Mr. Shawyer mentions in his presentation work on "new superconducting cavity desing" with Gilo Industries (2015).
Here is the link and the attachment:
https://goo.gl/ixUF72
or greater during a lifetime wouldn't need to be used, or they could be used in a more efficient manner. This direction could lead to a more materials stable device with a potential for a longer life and higher thrusts.
) that by imaginary time spupeng7 may be referring to this